Adelic Divisors on Arithmetic Varieties. (Record no. 127899)
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| fixed length control field | 04616nam a22004933i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4901863 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131324.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2016 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470429423 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470419264 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4901863 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4901863 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)948030438 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA242 .M86 2016 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.7/4 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Moriwaki, Atsushi. |
| 245 10 - TITLE STATEMENT | |
| Title | Adelic Divisors on Arithmetic Varieties. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (134 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.242 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Introduction -- 0.1. Birational Arakelov geometry -- 0.2. Green functions on analytic spaces over a compete discrete valuation field -- 0.3. Adelic arithmetic divisors -- 0.4. Main results -- 0.5. Conventions and terminology -- Chapter 1. Preliminaries -- 1.1. Lemmas -- 1.2. ℝ-Cartier divisors on a noetherian integral scheme -- 1.3. Analytification of algebraic schemes over a complete valuation field -- 1.4. Green functions on complex varieties -- Chapter 2. Adelic ℝ-Cartier Divisors over a Discrete Valuation Field -- 2.1. Green functions on analytic spaces over a discrete valuation field -- 2.2. Definition of adelic ℝ-Cartier divisors -- 2.3. Local degree -- 2.4. Local intersection number -- Chapter 3. Local and Global Density Theorems -- 3.1. Vertical fractional ideal sheaves and birational system of models -- 3.2. Model functions -- 3.3. Density theorems -- 3.4. Zariski's lemma for integrable functions -- 3.5. Radon measure arising from local intersection number -- Chapter 4. Adelic Arithmetic ℝ-Cartier Divisors -- 4.1. Definition and basic properties -- 4.2. Global degree -- 4.3. Volume of adelic arithmetic ℝ-Cartier divisors -- 4.4. Positivity of adelic arithmetic ℝ-Cartier divisors -- 4.5. Global intersection number -- Chapter 5. Continuity of the Volume Function -- 5.1. Basic properties of the volume -- 5.2. Proof of the continuity of the volume function -- 5.3. Applications -- Chapter 6. Zariski Decompositions of Adelic Arithmetic Divisors on Arithmetic Surfaces -- 6.1. Local Zariski decompositions of adelic divisors on algebraic curves -- 6.2. Proof of Zariski decompositions for adelic arithmetic divisors -- Chapter 7. Characterization of Nef Adelic Arithmetic Divisors on Arithmetic Surfaces -- 7.1. Hodge index theorem for adelic arithmetic divisors -- 7.2. Arithmetic asymptotic multiplicity. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 7.3. Necessary condition for the equality ̂ =̂ ᵪ -- 7.4. Numerical characterization -- Chapter 8. Dirichlet's unit Theorem for Adelic Arithmetic Divisors -- 8.1. Fundamental question for adelic divisors -- 8.2. Proof of Theorem 8.1.2 -- Appendix A. Characterization of Relatively Nef Cartier Divisors -- A.1. Asymptotic multiplicity -- A.2. Sectional decomposition -- A.3. Characterization in terms of _{ } -- Bibliography -- Subject Index -- Symbol Index -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | In this article, the author generalizes several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors, Zariski decompositions for arithmetic divisors on arithmetic surfaces and a special case of Dirichlet's unit theorem on arithmetic varieties, to the case of the adelic arithmetic divisors. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Divisor theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Topological groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algebraic varieties. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Approximation theory. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Moriwaki, Atsushi |
| Title | Adelic Divisors on Arithmetic Varieties |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2016 |
| International Standard Book Number | 9781470419264 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901863">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901863</a> |
| Public note | Click to View |
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